SOLUTION: Prove that (sin³A + cos³A)/(sinA + cosA) + (sin³A - cos³A)/(sinA - cosA) = 2

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Question 1136231: Prove that (sin³A + cos³A)/(sinA + cosA) + (sin³A - cos³A)/(sinA - cosA) = 2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that


use Factoring a Sum of Cubes rule:

a%5E3+%2B+b%5E3+=+%28a+%2B+b%29%28a%5E2+-+ab+%2B+b%5E2%29
.........simplify







sin%5E2%28A%29+%2B+cos%5E2%28A%29+%2B+sin%5E2%28A%29+%2B+cos%5E2%28A%29+=+2+

2%28sin%5E2%28A%29+%2B+cos%5E2%28A%29%29+=+2+

2%281%29+=+2+

2++=+2+